Algebraic Expansions: Broadening the Scope of Architectural Design through Algebraic Surfaces
Introduction: An Expanded Architectural Design Vocabulary
We conduct a design research project that radicalizes the relationship between tools and design possibilities: we significantly expand the architectural design vocabulary by employing mathematics and computer science as vehicles for accessing shapes that otherwise would be unthinkable: algebraic surfaces, the zero-sets of certain polynomials.
Algebraic surfaces can exhibit geometric features that cannot - or have so far not - be found in nature: puzzling convolutions in which complex geometry and topology combine with high degrees of tautness, harmony and coherence (Fig.1). Albeit mostly curved, they can contain straight lines and any number of plane curves (Fig.1, 1-3). They also look different from every direction, a quality we propose to call polyoptical from the Greek for an object with many faces. Having been studied in mathematics for the last two centuries they became accessible for designers only recently via advances in computer technology. This means a cambrian explosion of shapes, a whole zoo of new exotic shapes.
KeywordsMathematical Object Algebraic Surface Subdivision Surface NURBS Surface Large Vocabulary
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